Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematics of radio engineering wikipedia , lookup
Location arithmetic wikipedia , lookup
Elementary arithmetic wikipedia , lookup
Collatz conjecture wikipedia , lookup
Mathematical anxiety wikipedia , lookup
Positional notation wikipedia , lookup
Division by zero wikipedia , lookup
Math 008 - Cooley Prealgebra OCC Section 4.2 – Understanding Fractions Definition – Fraction A numerical representation indicating the quotient of two numbers (a numerator and a denominator). This 3 representation is a number that can represent part of a whole. For example: . Here, 3 is called the numerator, 5 5 is called the denominator, and both are separated by a line called the fraction bar. Division Involving the Number 1 and the Number 0 9 1 9 7 2) Any number divided by 1 remains unchanged. Example: 7 1 1) Any nonzero number divided by itself is 1. Example: 3) Zero may be divided by any nonzero number; the result is always zero. Example: 4) You cannot divide by zero. Example: 0 0 5 3 0 is undefined. (Note: is indeterminate.) 0 0 Proper Fraction A fraction whose numerator is always less than the denominator. Examples: 3 4 9 , , 5 7 31 Improper Fraction A fraction whose numerator is always greater than or equal to the denominator. Examples: 6 7 8 13 , , , 5 3 8 9 Mixed Number 3 7 8 The sum of a whole number greater than zero and a proper fraction. Examples: 2 ,4 ,13 5 9 13 Picture Representations of Improper Fractions Changing a Mixed Number to an Improper Fraction 1. Multiply the whole number by the denominator of the fraction. 2. Add the numerator of the fraction to the product found in step 1. 3. Write the sum found in step 2 over the denominator of the fraction. Changing an Improper Fraction to a Mixed Number 1. Divide the numerator by the denominator. 2. Write the quotient followed by the fraction with the remainder over the denominator. quotient remainder denominator -1- Math 008 - Cooley Prealgebra OCC Section 4.2 – Understanding Fractions Exercises: What fraction is represented by the darker shaded portion of the following figures? 1) 2) 3) Divide, if possible. Assume all variables in the denominators are nonzero. 4) 4 0 5) 0 6 6) 9 9 7) x x Answer the questions in the following applications. 8) Jillian earned $165 over the weekend at her waitressing job. She used $48 of it to repay a loan to her sister. What fractional part of her earnings did Jillian use to repay her sister? 9) In 2010, Orange Coast College had 21 full-time math instructors and 38 part-time math instructors. What fractional part of the faculty are part time? Change each mixed number to an improper fraction. 10) 2 3 5 11) 6 6 7 9 10 12) 7 16) 59 7 1 9 13) 6 17) 106 9 Change each improper fraction to a mixed number. 14) 13 5 15) 19 3 -2-